Mathematical and Numerical Modeling of the Cardiovascular System and Applications

The book comprises contributions by some of the most respected scientists in the field of mathematical modeling and numerical simulation of the human cardiocirculatory system. It covers a wide range of topics, from the assimilation of clinical data to the development of mathematical and computational models, including with parameters, as well as their efficient numerical solution, and both in-vivo and in-vitro validation. It also considers applications of relevant clinical interest. This book is intended for graduate students and researchers in the field of bioengineering, applied mathematics, computer, computational and data science, and medicine wishing to become involved in the highly fascinating task of modeling the cardiovascular system.

Autorentext

Daniele Boffi has been Professor of Numerical Analysis at the Department of Mathematics of the University of Pavia since 2005. He received his PhD in Mathematics from the Universities of Brescia-Milano-Pavia, Italy (1996). He has been a Visiting Professor at several institutions. His primary research interests are related to the numerical approximation of partial differential equations, including mixed finite elements, eigenvalue problems, computational electromagnetism, and the interaction of fluids and solids.

Luca F. Pavarino is Professor of Numerical Analysis at the Department of Mathematics of the University of Pavia. He holds a PhD (1992) and Master's (1990) in Mathematics from the Courant Institute, NYU, USA and a B.S. degree (1987) in Mathematics from the University of Pavia. He was a Postdoctoral Research Associate at Rice University, USA and Professor at the University of Milan. His current research focuses on domain decomposition methods for PDEs, parallel computing and biomathematics.

Gianluigi Rozza is Full Professor of Numerical Analysis and Scientific Computing at SISSA, International School for Advanced Studies. He holds a degree in Aerospace Engineering from Politecnico di Milano (2002) and a PhD in Applied Mathematics from Ecole Polytechnique Federale de Lausanne (2005). He was a Postdoctoral Research Associate at the Massachusetts Institute of Technology (MIT) Center for Computational Engineering (2006-08), then a Researcher and Lecturer at EPFL (2008-2012). He is the author of over 100 scientific publications and recipient of the 2014 ECCOMAS young investigator Jacques Louis Lions Award in Computational Mathematics for researchers under the age of 40. Professor Rozza has been an Associate Editor of the SIAM/ASA Journal of Uncertainty Quantification since 2013, of the SIAM Journal of Numerical Analysis since 2015, and of Computing and Visualization in Science since 2016.

Simone Scacchi is Associate Professor of Numerical Analysis at the Department of Mathematics of the University of Milan. He received a degree in Mathematics from the University of Milan (2004) and a PhD in Mathematics and Statistics from the University of Pavia (2008). He was a Postdoctoral Research Associate at the University of Pavia (2008) and then Assistant Professor at the University of Milan (2008-2015).

Christian Vergara has been Associate Professor of Numerical Analysis at MOX, Dipartimento di Matematica, Politecnico di Milano since 2015. He received a PhD in Mathematical Engineering from Politecnico di Milano in 2006. His primary research interests are the numerical approximation of fluid-structure interaction problems, the numerical modeling of the cardiovascular system, both in terms of blood dynamics and electrical activity of the heart, and the application to cases of clinical interests.

Inhalt
1 Daniele Boffi, Lucia Gastaldi, and Luca Heltai, A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids.- 2 Jessica Cervi and Raymond J. Spiteri, High-Order Operator-Splitting Methods for the Bidomain and Monodomain Models.- 3 Piero Colli Franzone, Luca F. Pavarino, and Simone Scacchi, Electro-mechanical modeling and simulation of reentry phenomena in the presence of myocardial infarction.- 4 Lorenzo Fassina, Marisa Cornacchione, Maria Evelina Mognaschi, Giovanni Magenes, and Fabio Naro, Ergotropic effect in cardiac tissue after electromagnetic and beta-adrenergic stimulus.- 5 Emilio Macchi, Ezio Musso, and Stefano Rossi, Role of electrotonic current in excitable cells.- 6 Andrea Manzoni, Diana Bonomi, and Alfio Quarteroni, Reduced order modeling for cardiac electrophysiology and mechanics: new methodologies, challenges & perspectives.- 7 Michele Conti, Simone Morganti, Alice Finotello, Rodrigo M. Romarowski, Alessandro Reali, and Ferdinando Auricchio, Aortic Endovascular Surgery.- 8 Marco Tezzele, Francesco Ballarin, and Gianluigi Rozza, Combined parameter and model reduction of cardiovascular problems by means of active subspaces and POD-Galerkin methods.- 9 Christian Vergara and Stefano Zonca, Extended Finite Elements method for fluid-structure interaction with an immersed thick non-linear structure.